As is well known, an optical frequency comb may be generated by providing a short or ultrashort laser pulse. Such a laser pulse may have a pulse period in the range of picoseconds to femtoseconds. However, even longer or smaller pulse periods are possible, for instance in the range of attoseconds to microseconds.
In the frequency domain, a sequence of laser pulses may be represented as a frequency comb. FIG. 2 illustrates such a representation in the form of a frequency comb, wherein the optical intensity I is plotted against the frequency f. The frequency comb comprises modes of discrete optical frequencies fm. An envelope of the intensity progression may lie within the amplification band width of a laser medium that generates the laser pulse. The width of the envelope is inversely proportional to the pulse period of the laser pulse.
As is well known, the frequencies of the modes of an optical frequency comb may be generally described by the formula fm=m×frep+f0 with m being a natural number and frep and f0 having the measurement unit of a frequency. As is evident from this formula and FIG. 2, the frequencies of adjacent modes of the optical frequency comb have the spacing frep referred to as a mode spacing of the frequency comb. When the frequency comb corresponds to a laser pulse circulating in a resonator, the mode spacing frep corresponds to the pulse repetition frequency (=repetition rate) of the oscillator, that is, the inverse of the round trip time of the pulse in the oscillator.
Usually, the modes of the frequency comb are not exactly an integer multiple of frep. As is evident from the above formula and FIG. 2, the frequency comb may be offset by an offset frequency f0. There may, however, also exist the case where f0 is equal to 0 and, thus, the modes of the frequency comb are integer multiples of frep. For a laser pulse circulating in a resonator, the presence of the offset frequency f0 may have its reason in the fact that the group velocity of a pulse circulating in the oscillator is different from the phase velocity of the individual modes of the pulse.
It is evident to the skilled person that the description of the modes of the frequency comb by the formula fm=m×frep+f0 is an idealized representation. The modes of a real frequency comb may have a finite width in the frequency domain.
Optical frequency combs may be used, for instance, in the area of spectroscopy, in particular, the spectroscopy of electronic transitions in atoms or for highly precise frequency measurements. For these applications, it is important to be able to stabilize a frequency comb. “Stabilizing a frequency comb” in the context of the present invention is to mean a stabilizing of the position of at least one of the modes of the frequency comb. An active stabilizing may be necessary, since the mode spacing frep and the offset frequency f0 may respond very sensitively to an external influence. For a laser pulse in a resonator, even a minute change of the resonator length and, thus, of the repetition rate, results in a change of the mode spacing frep of the frequency comb. A change of the offset frequency f0 may, for instance, be caused by a change of the dispersive characteristics in the resonator.
DE 199 11 103 A1 and DE 100 44 404 A1 disclose the stabilizing of optical frequency combs by controlling the two parameters, i.e., the frequency f0 and the mode spacing fm. DE 199 11 103 A1 discloses to change the resonator length by means of a movable deflection mirror so as to control the mode spacing of the frequency comb. Moreover, it is disclosed that the offset frequency may be adjusted by tilting a resonator mirror or by inserting a pair of prisms into the optical path of the resonator.
After providing the frequency comb, the parameters of the frequency comb (offset frequency f0 and mode spacing frep) may be undetermined. Generally, immediately after providing the frequency comb, at least one of these parameters is undetermined. Also during operation of the frequency comb, at least one of the parameters may be undetermined or may become undetermined, for instance, due to a change of a physical constraint.
Known control loops for stabilizing the frequency comb may be activated in a non-reliable manner only. The reason for this is that the usual control loop may stabilize a parameter of a frequency comb only when it is already (incidentally) within a range defined by the characteristics of the control loop. Otherwise, the control loop will typically begin oscillating, run to a limit of its control range, or control the frequency comb on the basis of a noise signal.